Interacting Droplets: Collective Dynamics - Towards Autonomous Soft Matter Systems - page 102

Fig. 7.7 Droplet squirmers have attractive interactions with walls. To p Representative squirmer
paths (for 3 different squirmers) near a wall ( black dashed line ). Bottom The number of droplets
as a function of the distance from the wall for an experiment as shown in the inset . The average
droplet diameter is 50 microns and the black arrow points to the wall in the image. Each point on
the curve is an average over 1500 time points

been shown that hydrodynamic interactions can explain the attractive interactions of
the so called dipolar swimmers with walls [ 24 ].
The droplet squirmers are also observed to aggregate at walls. In this section, we
do not seek to clarify the hydrodynamics of these interactions. Instead we utilize
this behavior, in combination with the fact that the droplet squirmer is simply a non-
equilibrium entity, to demonstrate passive rectification. In the top panel of Fig. 7.7 ,
the tracks of three droplets squirmers near a wall (dashed line) are shown. It is readily
seen that the droplets tend to travel along the wall for extended lengths, which are
much larger than the typical persistence lengths in regions away from walls. The
bottom panel of Fig. 7.7 shows the number of droplets plotted as a function of the
distance from a side wall for the image shown in the inset. The mean droplet size
in the experiment is 50

m. The vertical error bars represent the statistics on 1500
different time frames of the experiment. The horizontal error bars are one droplet
diameter across. This comes from the counting algorithm in which we segment the
image into strips of 75

μ

μ m width to count the droplets and a half droplet is not

a symmetry hyperplane, with the purpose of facilitating the solution of the original problem. In
electrostatics, for example, it can be used to calculate the electric field of a charge in the vicinity of
a conducting surface.